The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  0  1  1  6  1  1 12  1 10  1  1  1  1  1  0  1  1  1 12  1  6  1  1  1 10  1  1  1  1  1  1  1  2  1  1  0  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  1  0  5  1  6  3  1 15  1 12 10  9  3  0  1  6  5 12  1 10  1 15  6  9  1  0  5  3  9 12  5 10 12  0  9  1  3  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  0  8  0  8  8  8  0  8  0  8  8  8  8  8  8  0  8  8  0  0  0  8  8  8  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  8  0  8  0  0  8  8  8  8  0  0  8  8  8  8  8  8  0  8  8  0  0  8  0  0  8  0  8  0  0  8  0  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  8  0  0  0  0  0  8  8  0  8  8  0  0  8  8  8  0  8  0  8  8  0  8  0  0  0  8  0  8  8  8  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  0  8  8  8  0  8  8  0  0  8  0  8  0  8  8  0  0  8  0  0  8  0  0  0  8  0  0  8  8  0  8  0  8  0
 0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  0  8  8  0  8  0  8  0  8  8  8  8  0  0  8  8  0  0  8  0  0  8  8  8  8  8  8  0  0  0  8  8  0  0
 0  0  0  0  0  0  0  8  0  8  0  0  0  0  0  0  8  8  0  8  0  8  8  8  8  8  8  0  0  8  8  0  8  8  0  0  8  0  8  8  8  8  8  0  0  0  8  0  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  0  8  8  0  8  8  8  8  0  0  0  0  0  0  0  8  8  0  0  0  0  8  8  8  8  8  8  0  0  8  0  0

generates a code of length 50 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+33x^40+36x^41+71x^42+156x^43+248x^44+666x^45+989x^46+3172x^47+2300x^48+7252x^49+3000x^50+7180x^51+2305x^52+3200x^53+966x^54+716x^55+199x^56+104x^57+67x^58+40x^59+22x^60+6x^61+13x^62+9x^64+14x^66+1x^68+2x^72

The gray image is a code over GF(2) with n=400, k=15 and d=160.
This code was found by Heurico 1.16 in 9.37 seconds.